How to draw the graph of $y=(2x^2+13x+9)/(6x+3)$

Question

We haven't learnt how to design the graphic when the denominator has x, and it cannot be simplified. Can you just tell me the steps or lead me to a web address?

Answer 1

Let $f(x)=\frac{2x^2+13x+9}{6x+3}$ and try to find the values of $f$ for different values of $x$, find these pairs on and x-y axis and you will have a picture of this function:

and more and more points:

of course comments above are very helpful.